This article demonstrates a novel combination of solvent absorption, membrane desorption and microalgal cultivation to capture carbon dioxide and convert it to a lipid-rich biomass. In the system, carbon dioxide is absorbed into a potassium carbonate solvent and this gas is desorbed directly into the microalgal medium via a non-porous polydimethyl siloxane (PDMS) hollow fibre membrane. This single step approach provides a paradigm shift in the cost of carbon delivery to the microalgae, as the very large reboiler energy demand of standard carbon capture solvent regeneration is avoided, as is the energy associated with gas compression. Specifically, the use of a 20 wt% potassium carbonate solvent with 0.2, 0.5 and 0.7 CO₂ loading was evaluated as a mechanism to deliver carbon dioxide to cultures of a salt tolerant Chlorella sp. microalgae. In all cases, accelerated growth of Chlorella sp. was observed, relative to a control. The use of carbonate solutions of 0.5 and 0.7 loading resulted in the highest volumetric productivity (0.38 g L⁻¹ d⁻¹) and biomass concentration (1.8 g L⁻¹) by completely avoiding carbon limitation of the cultures. The system has demonstrated potential for the generation of biofuels that utilise carbon dioxide generated from power station flue gases with minimal parasitic energy demand.